For the multi-target DOA estimation problem of uniform linear arrays, this paper proposes a DOA estimation method based on the deep convolution neural network. The algorithm adopts the deep convolutional neural network, and the DOA estimation problem of the array signal is transformed into the inverse mapping problem of the array output covariance matrix to a binary sequence in which “1” indicates that there is a target incident in the corresponding angular direction at that position. The upper triangular array of the discrete covariance matrix is used as the data input to realize the DOA estimation of multiple sources. The simulation results show that the DOA estimation accuracy of the proposed algorithm is significantly better than that of the typical super-resolution estimation algorithm under the conditions of low SNR and small snapshot. Under the conditions of high SNR and large snapshot, the estimation accuracy of the proposed algorithm is basically the same as those of the MUSIC algorithm, ESPRIT algorithm, and ML algorithm, which are better than that of the deep fully connected neural network. The analysis of the simulation results shows that the algorithm is effective, and the time and space complexity can be further reduced by replacing the square array with the upper triangular array as the input.

Enhancing the degrees of freedom (DOFs) of MIMO systems has been a hotspot in communications. In this letter, a novel strategy to construct difference coarray of the sum coarray (DCSC) with heightened DOFs for coprime MIMO systems is put forward. Using the polynomial of DCSC, we reveal that DOFs expansion for sparse MIMO systems is a replicate-and-shift (RS) procedure, which explains the deficiency of overlapping lags caused by the consecutive DOFs in the difference coarray (DCA) as a moving period. To tackle this problem, the moving period is raised to the number of DOFs, so that the lags and holes in the forward and backward periods can perfectly complement each other. The range of consecutive DOFs (cDOFs) and the number of DOFs are then described in the closed-form expressions. The results show that the proposed strategy generates more DOFs than previous studies.

In recent years, sparse arrays have made considerable strides in resolving uncorrelated sources. However, the ubiquitous coherent sources across various emerging applications pose unique challenges for direction-of-arrival (DOA) estimation with sparse arrays. In this work, based on insight into the structure of the source covariance matrix, we first propose an effective strategy to achieve decorrelation by partitioning the diagonal and off-diagonal elements in the source covariance matrix. Then, we introduce two Toeplitz matrix reconstruction programs tailored for DOA estimation with sparse arrays. On one hand, we directly implement the decorrelation operation on the covariance matrix of sparse arrays, and further construct a Toeplitz matrix reconstruction program via virtual array interpolation for enhanced DOA estimation. On the other hand, we relate the sparse array to the hypothetical uniform linear array (ULA) through the compressed matrix, and perform decorrelation operation on the covariance matrix of the hypothetical ULA. Following this, a Toeplitz matrix reconstruction program via physical array interpolation is formulated for DOA estimation. Unlike the prevailing decorrelation techniques, the proposed algorithms can precisely estimate coherent sources without losing degrees of freedom and array aperture. Moreover, the Cramér-Rao bound pertinent to this problem is derived. Numerical simulations demonstrate that the proposed algorithms outperform their competitors in estimating coherent sources.

Coprime array (CA) is a highly regarded sparse geometry for direction of arrival (DOA) estimation because it offers heightened degrees of freedom (DOF) and alleviated mutual coupling (MC) effect. Nevertheless, the appearance of holes in the difference co-array (DCA) of CA extremely shortens the continuous DOF (cDOF) available for spatial smoothing technique. To cope with this deficiency, we develop an augmented coprime array (ACA) in this paper by deploying a uniform subarray and one sensor at the left end and right end of CA, respectively. The placement of these additional sensors is determined by the analytical expressions and a two-dimensional (2D) representation that account for all the holes in the DCA of CA. The precise mathematical expressions for the attainable DOF and the first three weight functions of ACA are further derived, which show that ACA achieves the equivalent quantity of cDOF as the hole-free (super) nested arrays, while retaining a comparable level of MC effect to CA. Moreover, in comparison to the majority of advanced sparse array geometries, the devised ACA proves more effective at striking a balance between the quantity of cDOF and MC effect. Numerical examples are provided to confirm the outstanding characteristics of our designed ACA and its remarkable efficacy in DOA estimation.

This paper proposes a joint estimation method for source number and DOA based on an improved convolutional neural network for unknown source number and undetermined DOA estimation. By analyzing the signal model, the paper designs a convolutional neural network model based on the existence of a mapping relationship between the covariance matrix and both the source number and DOA estimation. The model, which discards the pooling layer to avoid data loss and introduces the dropout method to improve generalization, takes the signal covariance matrix as input and the two branches of source number estimation and DOA estimation as outputs, and achieves the unfixed number of DOA estimation by filling in invalid values. Simulation experiments and analysis of the results show that the algorithm can effectively achieve the joint estimation of source number and DOA. Under the conditions of high SNR and a large snapshot number, both the proposed algorithm and the traditional algorithm have high estimation accuracy, while under the conditions of low SNR and a small snapshot, the algorithm is better than the traditional algorithm, and under the underdetermined conditions, where the traditional algorithm often fails, the algorithm can still achieve the joint estimation.

A novel generalized nested multiple-input multiple-output (MIMO) radar for direction of arrival (DOA) estimation is proposed in this paper. The proposed structure utilizes the extended two-level nested array (ENA) as transmitter and receiver and adjusts the interelement spacing of the receiver with an expanding factor. By optimizing the array element configuration, we can obtain the best number of elements of the transmitter and receiver and the attainable degrees of freedom (DOF). Compared with the existing nested MIMO radar, the proposed MIMO array configuration not only has closed-form expressions for sensors’ positions and the number of maximum DOF, but also significantly improves the array aperture. It is verified that the sum-difference coarray (SDCA) of the proposed nested MIMO radar can get higher DOF without holes. MUSIC algorithm based on Toeplitz matrix reconstruction is employed to prove the rationality and superiority of the proposed MIMO structure.